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Higher Mathematics
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Download or read book Easy as p? written by Oleg A. Ivanov and published by Springer Science & Business Media. This book was released on 1999 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction for readers with some high school mathematics to both the higher and the more fundamental developments of the basic themes of elementary mathematics. Chapters begin with a series of elementary problems, cleverly concealing more advanced mathematical ideas. These are then made explicit and further developments explored, thereby deepending and broadening the readers' understanding of mathematics. The text arose from a course taught for several years at St. Petersburg University, and nearly every chapter ends with an interesting commentary on the relevance of its subject matter to the actual classroom setting. However, it may be recommended to a much wider readership; even the professional mathematician will derive much pleasureable instruction from it.
Book Synopsis A Gateway to Higher Mathematics by : Jason H. Goodfriend
Download or read book A Gateway to Higher Mathematics written by Jason H. Goodfriend and published by Jones & Bartlett Learning. This book was released on 2005 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Gateway to Higher Mathematics integrates the process of teaching students how to do proofs into the framework of displaying the development of the real number system. The text eases the students into learning how to construct proofs, while preparing students how to cope with the type of proofs encountered in the higher-level courses of abstract algebra, analysis, and number theory. After using this text, the students will not only know how to read and construct proofs, they will understand much about the basic building blocks of mathematics. The text is designed so that the professor can choose the topics to be emphasized, while leaving the remainder as a reference for the students.
Book Synopsis An Accompaniment to Higher Mathematics by : George R. Exner
Download or read book An Accompaniment to Higher Mathematics written by George R. Exner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.
Book Synopsis Transition to Higher Mathematics by : Bob A. Dumas
Download or read book Transition to Higher Mathematics written by Bob A. Dumas and published by McGraw-Hill Education. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written for students who have taken calculus and want to learn what "real mathematics" is.
Book Synopsis A Bridge to Higher Mathematics by : Valentin Deaconu
Download or read book A Bridge to Higher Mathematics written by Valentin Deaconu and published by CRC Press. This book was released on 2016-12-19 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.
Book Synopsis Towards Higher Mathematics: A Companion by : Richard Earl
Download or read book Towards Higher Mathematics: A Companion written by Richard Earl and published by Cambridge University Press. This book was released on 2017-09-07 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.
Book Synopsis Higher Mathematics for Physics and Engineering by : Hiroyuki Shima
Download or read book Higher Mathematics for Physics and Engineering written by Hiroyuki Shima and published by Springer Science & Business Media. This book was released on 2010-04-12 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are: - Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis. This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.
Book Synopsis Bridge to Higher Mathematics by : Sam Vandervelde
Download or read book Bridge to Higher Mathematics written by Sam Vandervelde and published by Lulu.com. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging math textbook is designed to equip students who have completed a standard high school math curriculum with the tools and techniques that they will need to succeed in upper level math courses. Topics covered include logic and set theory, proof techniques, number theory, counting, induction, relations, functions, and cardinality.
Book Synopsis Contests in Higher Mathematics by : Gabor J. Szekely
Download or read book Contests in Higher Mathematics written by Gabor J. Szekely and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most effective ways to stimulate students to enjoy intellectual efforts is the scientific competition. In 1894 the Hungarian Mathematical and Physical Society introduced a mathematical competition for high school students. The success of high school competitions led the Mathematical Society to found a college level contest, named after Miklós Schweitzer. The problems of the Schweitzer Contests are proposed and selected by the most prominent Hungarian mathematicians. This book collects the problems posed in the contests between 1962 and 1991 which range from algebra, combinatorics, theory of functions, geometry, measure theory, number theory, operator theory, probability theory, topology, to set theory. The second part contains the solutions. The Schweitzer competition is one of the most unique in the world. The experience shows that this competition helps to identify research talents. This collection of problems and solutions in several fields in mathematics can serve as a guide for many undergraduates and young mathematicians. The large variety of research level problems might be of interest for more mature mathematicians and historians of mathematics as well.
Book Synopsis Advanced Problems in Mathematics by : Stephen Siklos
Download or read book Advanced Problems in Mathematics written by Stephen Siklos and published by . This book was released on 2019-10-16 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.
Book Synopsis Introduction to Higher Algebra by : Maxime Bôcher
Download or read book Introduction to Higher Algebra written by Maxime Bôcher and published by . This book was released on 1907 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Transition to Advanced Mathematics by : William Johnston
Download or read book A Transition to Advanced Mathematics written by William Johnston and published by Oxford University Press. This book was released on 2009-07-27 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.
Book Synopsis Higher Mathematics from an Elementary Point of View by : RADEMACHER
Download or read book Higher Mathematics from an Elementary Point of View written by RADEMACHER and published by Birkhäuser. This book was released on 2013-09-11 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Course of Higher Mathematics by : Vladimir Ivanovich Smirnov
Download or read book A Course of Higher Mathematics written by Vladimir Ivanovich Smirnov and published by . This book was released on 1964 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts by : David C. Geary
Download or read book Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts written by David C. Geary and published by Academic Press. This book was released on 2017-08-01 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public
Book Synopsis Discovering Higher Mathematics by : Alan Levine
Download or read book Discovering Higher Mathematics written by Alan Levine and published by Academic Press. This book was released on 1999-10-29 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses. * Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization * Guidelines for effective mathematical thinking, covering a variety of interrelated topics * Numerous problems and exercises designed to reinforce the key themes
Book Synopsis Higher Mathematics for Engineering and Technology by : Mahir M. Sabzaliev
Download or read book Higher Mathematics for Engineering and Technology written by Mahir M. Sabzaliev and published by CRC Press. This book was released on 2018-05-03 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on and enriched by the long-term teaching experience of the authors, this volume covers the major themes of mathematics in engineering and technical specialties. The book addresses the elements of linear algebra and analytic geometry, differential calculus of a function of one variable, and elements of higher algebra. On each theme the authors first present short theoretical overviews and then go on to give problems to be solved. The authors provide the solutions to some typical, relatively difficult problems and guidelines for solving them. The authors consider the development of the self-dependent thinking ability of students in the construction of problems and indicate which problems are relatively difficult. The book is geared so that some of the problems presented can be solved in class, and others are meant to be solved independently. An extensive, explanatory solution of at least one typical problem is included, with emphasis on applications, formulas, and rules. This volume is primarily addressed to advanced students of engineering and technical specialties as well as to engineers/technicians and instructors of mathematics. Key features: Presents the theoretical background necessary for solving problems, including definitions, rules, formulas, and theorems on the particular theme Provides an extended solution of at least one problem on every theme and guidelines for solving some difficult problems Selects problems for independent study as well as those for classroom time, taking into account the similarity of both sets of problems Differentiates relatively difficult problems from others for those who want to study mathematics more deeply Provides answers to the problems within the text rather than at the back of the book, enabling more direct verification of problem solutions Presents a selection of problems and solutions that are very interesting not only for the students but also for professor-teacher staff
